With the advent of global positioning system (GPS) and the increasing expansion of technology, improving GPS receivers positioning has attracted great attention. When the signal received by these receivers is weak, receiver functioning becomes impaired. Due to the existing noise and the presence of Doppler shift in weak signal conditions, the signal acquisition section becomes problematic and in weak signal conditions or phase lock loop (PLL), the tracking section design of noise conditions gets difficult. In case of a lock loss on the signal, the user will not be able to calculate the Doppler frequency and the system will diverge. Therefore, a robust algorithm for the GPS receiver PLL is very vital. In this paper, the squared segmented matched filter-fast Fourier transform algorithm is used to improve the acquisition of weak GPS signals with an average SNR of 15 dB. By using the matched filter, the SNR is maximized and the code phase estimation will be more accurately. Also, the use of a segmented filter before the FFT reduces the number of FFT points and therefore, the computational complexity is reduced. To calculate the number of batches and obtain the best acquisition output, in the proposed algorithm, the system becomes fuzzy. In tracking section, fractional Fourier transform (FRFT) with the PLL based on fuzzy Kalman filter (FKF) is used to reinforce it against weak signal environments. The FRFT is used for estimating frequency and acceleration, and a third-order FKF is used for designing the PLL. As a result of these changes, the RMSE of positioning is improved more than 35%.

随着全球定位系统（GPS）的出现以及技术的不断扩展，改善GPS接收机的定位引起了人们的极大关注。当这些接收器接收到的信号较弱时，接收器的功能会受损。由于在弱信号条件下存在噪声并存在多普勒频移，因此信号采集部分会出现问题，而在弱信号条件或锁相环（PLL）下，噪声条件的跟踪部分设计会变得困难。万一信号失锁，用户将无法计算多普勒频率，并且系统会发散。因此，用于GPS接收器PLL的鲁棒算法至关重要。在本文中，平方分段匹配滤波快速傅立叶变换算法用于改善平均SNR为15 dB的弱GPS信号的获取。通过使用匹配滤波器，可以使SNR最大化，并且代码相位估计将更加准确。而且，在FFT之前使用分段滤波器减少了FFT点的数量，因此降低了计算复杂度。为了计算批数并获得最佳的采集输出，在所提出的算法中，系统变得模糊。在跟踪部分，使用基于模糊卡尔曼滤波器（FKF）的带锁相环的分数阶傅里叶变换（FRFT）来增强其抗弱信号环境的能力。FRFT用于估计频率和加速度，而三阶FKF用于设计PLL。由于这些变化，